Question: Given $ m \angle RPS = 5x + 26$, and $ m \angle QPR = 6x - 66$, find $m\angle QPR$. $P$ $Q$ $S$ $R$
Answer: From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Since $\angle QPS$ is a straight angle, we know ${m\angle QPS = 180}$ Substitute in the expressions that were given for each measure: $ {6x - 66} + {5x + 26} = {180}$ Combine like terms: $ 11x - 40 = 180$ Add $40$ to both sides: $ 11x = 220$ Divide both sides by $11$ to find $x$ $ x = 20$ Substitute $20$ for $x$ in the expression that was given for $m\angle QPR$ $ m\angle QPR = 6({20}) - 66$ Simplify: $ {m\angle QPR = 120 - 66}$ So ${m\angle QPR = 54}$.